How to do long division, step by step

What is long division?

Long division is a way of dividing by a two-digit number on paper, where every step of the working is written down under the number being divided. It does the same job as short division (the bus stop method), but instead of working out the leftovers in your head and carrying them, you write each multiplication and subtraction out in full. That makes it easier to divide by numbers like 24 or 37, whose multiples most of us don't know by heart.

A few words help. The number being divided is the dividend, the number you divide by is the divisor, and the answer is the quotient.

How to do long division, step by step

To do long division, write the divisor to the left of the bus stop and the number you're dividing underneath it. Then work from the left:

1. Divide. How many times does the divisor go into the first digit, or the first two digits? Write that above.
2. Multiply. Multiply the divisor by that number and write the answer underneath.
3. Subtract. Take it away to find what's left over.
4. Bring down the next digit next to what's left, and go back to step 1.

When there are no digits left to bring down, what's left over is the remainder. Here's a four-digit number divided by a two-digit number, with nothing left over.

1. 24 doesn't go into 8, so start with 85. How many 24s in 85? 3, because 3 × 24 = 72. Write 3 above, then 85 − 72 = 13.
2. Bring down the 6 to make 136. How many 24s in 136? 5, because 5 × 24 = 120. Write 5 above, then 136 − 120 = 16.
3. Bring down the 8 to make 168. How many 24s in 168? 7, because 7 × 24 = 168. Write 7 above, then 168 − 168 = 0.
4. Nothing left over, so 8,568 ÷ 24 = 357.

Schools set long division out in slightly different ways, and some children write a minus sign beside each subtraction, which the national curriculum mentions. Follow the layout your child has been taught.

Write out the multiples of the divisor first

A useful tip is to write out the first few multiples of the divisor before starting, so the "how many?" question at each step is a matter of looking it up. For 8,568 ÷ 24, the list starts 24, 48, 72, 96, 120, 144, 168, 192 and 216.

Each multiple is 24 more than the one before, 48 is double 24, and 10 × 24 = 240 makes a handy check at the end. Then, at each step, they pick the biggest multiple that fits. For 85, that's 72, because 96 is too big.

Long division with remainders

When the divisor doesn't go in exactly, there's a remainder: the amount left at the end, with nothing more to bring down. It must always be smaller than the divisor.

1. 15 doesn't go into 4, so start with 43. How many 15s in 43? 2, because 2 × 15 = 30. Write 2 above, then 43 − 30 = 13.
2. Bring down the 5 to make 135. How many 15s in 135? 9, because 9 × 15 = 135. Write 9 above, then 135 − 135 = 0.
3. Bring down the 7 to make 7. How many 15s in 7? None, so write 0 above.
4. Nothing left to bring down, so the answer is 290 remainder 7.

How to interpret remainders

The Year 6 curriculum asks children to give a remainder in one of three ways, depending on what the question needs. Take 4,357 books packed in boxes of 15:

Way	Answer	When it fits
As a whole number remainder	290 remainder 7	The question asks how many full boxes and how many books are left over
As a fraction	290 and seven fifteenths	The remainder is shared out, so there are seven fifteenths of a box more
By rounding	290 or 291	How many full boxes? 290. How many boxes are needed for every book? 291

Rounding is where word problems catch children out. Rounding up is right when everything has to fit in, like the boxes. Rounding down is right when only complete groups count, like the full boxes.

When there's a zero in the answer

Sometimes the divisor doesn't go into the number made by bringing down a digit. When that happens, write 0 in the answer and bring down the next digit as well.

1. 24 doesn't go into 7, so start with 72. How many 24s in 72? 3, because 3 × 24 = 72. Write 3 above, then 72 − 72 = 0.
2. Bring down the 4 to make 4. How many 24s in 4? None, so write 0 above.
3. Bring down the 8 to make 48. How many 24s in 48? 2, because 2 × 24 = 48. Write 2 above, then 48 − 48 = 0.
4. Nothing left over, so 7,248 ÷ 24 = 302.

Leaving out the zero is a common slip. It would give 32, not 302, which a quick estimate shows is far too small: 7,248 is roughly 7,200, and 7,200 ÷ 24 = 300.

Estimate and check

An estimate before starting, and a check afterwards, catch most mistakes. The Year 6 curriculum asks children to use estimation to check their answers.

• Estimate. Round to numbers that are easy to divide. For 8,568 ÷ 24, 24 is close to 25, and there are four 25s in every 100, so 8,500 ÷ 25 = 340. The answer, 357, is close.
• Check with the inverse. Multiply the answer by the divisor, then add any remainder: 357 × 24 = 8,568. For the example with a remainder, 290 × 15 = 4,350, and 4,350 + 7 = 4,357. Our long multiplication guide shows how to do the multiplication.

Long division or short division?

Short division is enough when your child can work out each step in their head. That's always true for a one-digit divisor, which children divide by with short division in Year 5. The Year 6 curriculum also asks them to use short division for a two-digit divisor where appropriate, for example dividing by 11 or 12, whose multiples they know from the 11 times table and 12 times table.

Long division is the better choice when the multiples of the divisor aren't known by heart, like 24, 37 or 56.

Some children also meet chunking, where they take away big chunks of the divisor, like 10 lots or 100 lots, until nothing is left. It's a good way to understand what division is doing. In the SATs, though, partial marks aren't given for chunking, as the section below explains.

Long division in Year 6 and the SATs

Long division is a Year 6 method. Children divide numbers with up to 4 digits by a two-digit number, and the curriculum expects them to be fluent in written methods for all four operations by the end of the year. See our Year 6 maths guide for what else comes in Year 6.

Long division comes up in Paper 1, the arithmetic paper, of the KS2 SATs. The KS2 mathematics test framework says most arithmetic questions are worth one mark, but two marks are available for long division. If the final answer is wrong, a mark can still be given for correct working using the formal method. Partial marks aren't given where the chunking method has been used. Our KS2 maths SATs guide has the dates and papers, and our free SATs arithmetic practice paper has two long division questions to try.

Common long division mistakes

• Leaving out a zero in the answer. When the divisor doesn't go in, a 0 still needs writing above.
• A remainder bigger than the divisor. If what's left is as big as the divisor, it goes in at least once more. Go back and try one more.
• Digits drifting out of their columns. Each digit of the answer goes above the last digit used. Squared paper helps.
• Bringing down two digits at once. Only bring down one digit each time.
• Subtraction slips. Each step uses column subtraction, so the same care with exchanging applies.
• Times table slips. Government guidance for teachers says the facts up to 9 × 9 are needed for written division, so a slow fact slows the whole method.

How to help at home

• Ask for an estimate first. "Roughly how big will the answer be?" before every division.
• Check with the inverse. Multiply back to see if it gives the starting number.
• Talk through remainders. Make up a quick problem with buses, boxes or teams and ask whether to round up or down.
• Keep the tables fresh. The times tables test mixes up every table, and our guide on how to learn times tables has a routine.

Long division questions to try

1. 672 ÷ 16
2. 4,836 ÷ 12
3. 5,184 ÷ 24
4. 9,135 ÷ 21
5. 2,000 ÷ 15, with the remainder as a whole number
6. 375 children go on a trip in coaches with 52 seats. How many coaches do they need?

Answers

1. 42
2. 403
3. 216
4. 435
5. 133 remainder 5
6. 8 coaches (375 ÷ 52 = 7 remainder 11, so 7 coaches aren't enough and the answer rounds up)